The former Genoa midfielder is regarded among the best young players in Italy.
"El Shaarawy is a very good player and he will become a No 1," Allegri said to La Gazzetta dello Sport.
"He is young, has quality, and he is of the type of player that you must focus on to create a cycle - and make us competitive in Europe too.
"We have to be careful though, you don't have to create a phenomenon.
"Stephan is still a young boy and he will have to study this new environment, but I'm convinced that he has his head in the right place.
"When Milan choose a player, they don't only look at his technical qualities "